Apparatus for winding a plurality of strips onto cores mounted on a common winding shaft are disclosed in the patents to Schmidt U.S. Pat. No. 3,425,395 and Ormsby U.S. Pat. No. 3,603,521. The Schmidt apparatus provides no opportunity for individual control of the clutch means and the structure disclosed therein is inherently expensive to manufacture and susceptible to breakdown. The Ormsby apparatus embodies a sophisticated control system for simultaneously adjusting the respective clutch assemblies and the speed of rotation of the winding shaft in response to signals which are proportional to the radius of the coils being wound so that it is not possible optionally to wind the strip material onto the cores at a constant tension or varying tension depending upon the width and/or thickness of material being wound. The apparatus of this invention is designed to enable employing existing slitting and winding equipment without drastic modification by employing specially designed electromagnet clutches on the drive shaft which can be controlled individually so as to enable winding strip material of different widths and varying thickness simultaneously at the same or different tensions; to provide for operating at lower winding speeds to avoid heating as the coils increase in size without change in tensions; to provide for positioning the coils at the same or different spacings along the winding shaft; and to provide for removing and remounting the cores and/or clutch assemblies on the drive shaft without major dismantling operations. The clutches are of the kind in which the torque is applied through magnetic particles confined between poles and are designed to provide for a very low starting torque if desired, an extensive range in torque, efficient transmission of the torque, minimum particle loss and minimum frictional losses and wear.